Merging two bones that are children of 'one' parent
If you want to delete, let say, bone1, and you want to keep, let say, bone2, with influence of bone1 being given to bone2, you can delete bone1, then go in the Properties panel > Object Data > Vertex Groups, select bone1 group, press Select, select bone2 group, press Assign, now the vertex group that was linked to bone1 is linked to bone2.